Ε-Henig saddle points and duality of set-valued optimization problems in real linear spaces

We study Ε-Henig saddle points and duality of set-valued optimization problems in the setting of real linear spaces. Firstly, an equivalent characterization of Ε-Henig saddle point of the Lagrangian set-valued map is obtained. Secondly, under the assumption of the generalized cone subconvexlikeness of set-valued maps, the relationship between the Ε-Henig saddle point of the Lagrangian set-valued map and the Ε-Henig properly efficient element of the set-valued optimization problem is presented. Finally, some duality theorems are given.